A most common facet of the molecular structure of biological systems is the separation of polar or ionic water-like components from less polar or oil-like components. This segregation is called the "hydrophobic effect," and the physical forces that produce it are called "hydrophobic interactions." The proposed research aims at using the theoretical methods of computer simulation and statistical mechanics to establish a quantitative understanding of the role of hydrophobic interactions in biology. Previous work provides a quantitative understanding of hydrophobic effects in much simpler contexts, such as solubility of oil in water, and the self-assembly of mesoscopic structures like micelles in liquid oil-water-surfactant mixtures. In biology, however, hydrophobic effects appear in systems that are highly heterogeneous, such as folded proteins. To reach the goal of this proposed research, computer simulations will be performed to examine the dynamics of a pair of proteins and their aqueous environment while the proteins assemble into a dimer due to hydrophobic interactions. Recently developed computational methods combined with the most powerful computers currently available make this work practical. Simulation results together with other numerical studies of much simpler model systems will be analyzed with modern methods of statistical physics to reach a general and quantitative understanding of protein-protein interactions. The final objective is to codify this understanding with simple and convenient equations that can be used to interpret the stability and kinetics of protein assembly. Proteins and protein complexes are nature's machines. Their many functions are central to life as we know it. Disease and death are ultimately due to malformed or malfunctioning proteins. The hydrophobic effect is arguably the most fundamental of physical forces orchestrating the structure of proteins and protein complexes. It is therefore central to health and life.